Answer:
previous balance
Step-by-step explanation:
General vertex form:
![y = m(x − a)² + b \: with \: vertex \: at \: (a, b)](https://tex.z-dn.net/?f=y%20%3D%20m%28x%20%E2%88%92%20a%29%C2%B2%20%2B%20b%20%20%5C%3A%20with%20%20%5C%3A%20vertex%20%5C%3A%20%20at%20%5C%3A%20%20%28a%2C%20b%29)
Given :
![y = 2x² + 5x - 3](https://tex.z-dn.net/?f=y%20%3D%202x%C2%B2%20%2B%205x%20%20-%203)
Extract "spread factor" m
![y = 2( x² + \frac{5}{2} x) - 3](https://tex.z-dn.net/?f=y%20%3D%202%28%20x%C2%B2%20%2B%20%20%5Cfrac%7B5%7D%7B2%7D%20x%29%20-%203)
Complete the square
![y = 2(x² + \frac{5}{2}x + ( \frac{5}{4})²) - 3](https://tex.z-dn.net/?f=y%20%3D%202%28x%C2%B2%20%20%2B%20%20%5Cfrac%7B5%7D%7B2%7Dx%20%2B%20%28%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2%29%20-%203)
![- 2( \frac{5}{4})²](https://tex.z-dn.net/?f=%20-%202%28%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2)
Write as a squared binomial and simplify the constant
![y = 2(x + \frac{5}{4})² - 6 \frac{1}{8}](https://tex.z-dn.net/?f=y%20%3D%202%28x%20%2B%20%20%5Cfrac%7B5%7D%7B4%7D%29%C2%B2%20-%206%20%5Cfrac%7B1%7D%7B8%7D%20)
Re-write to match signs of standard general form:
![y = 2(x - ( - \frac{5}{4}))² \: + ( - 6 \frac{1}{8})](https://tex.z-dn.net/?f=y%20%3D%202%28x%20-%20%28%20-%20%20%5Cfrac%7B5%7D%7B4%7D%29%29%C2%B2%20%5C%3A%20%20%2B%20%28%20-%206%20%5Cfrac%7B1%7D%7B8%7D%29)
I believe the answer is 2
The answer is x=1
x^5=1
x=5[square]1
x=1
I: y<2*x
II: y<8
III: x>2
a: (5,3):
I: 3<2*5
3<10 ?yes
II: 3<8 ?yes
III: 5>2 ?yes
This is a solution
b: (6,0):
I: 0<2*6
0<12 ?yes
II: 0<8 ?yes
III: 6>2 ?yes
This is a solution
c: (3,3):
I: 3<2*3
3<6 ?yes
II: 3<8 ?yes
III: 3>2 ?yes
This is a solution
d: (1,-4):
I: -4<2*1
-4<2 ?yes
II: -4<8 ?yes
III: 1>2 ?no
This is not a solution
e: (4,-2):
I: -2<2*4
-2<8 ?yes
II: -2<8 ?yes
III: 4>2 ?yes
This is a solution
f: (5,9):
I: 9<2*5
9<10 ?yes
II: 9<8 ?no
This is not a solution
so a,b,c,e are solutions and d,f not